How to Find Magnetic Field Direction Above and Below a Wire

A straight wire carries conventional current vertically upwards. What direction is the magnetic field directly above the wire? What about directly below it?

The answer is different at the two positions: **above the wire, the magnetic field points into the page; below the wire, it points out of the page**, provided the wire is drawn vertically upwards in the plane of the page.

The quickest reliable method is the **right-hand grip rule**. Point your right thumb in the direction of conventional current. Your curled fingers show the direction of the magnetic field circling the wire.

The important detail is that the magnetic field forms circles around the wire. It does not point in one constant direction everywhere. Moving from above the wire to below it takes you to the opposite side of the circular field, so the field direction reverses.

## 1. Finding the field direction above and below a straight wire

Imagine looking at a vertical wire drawn on a sheet of paper. Conventional current travels upwards, towards the top of the page.

Use your right hand as follows:

1. Point your right thumb upwards, in the direction of conventional current.
2. Curl your fingers naturally around the imaginary wire.
3. At each position around the wire, your curled fingers indicate the magnetic field direction.

For this particular arrangement:

| Position relative to the wire | Magnetic field direction |
|---|---|
| Directly to the right | Into the page |
| Directly to the left | Out of the page |
| Directly above | Into the page |
| Directly below | Out of the page |

There is a useful geometric detail here. The table describes a wire drawn vertically upwards in the plane of the page, with the observation positions on the page. The field circles around the wire in three dimensions, so the field at positions above and below the wire is perpendicular to the page.

[IMAGE: Three-dimensional annotated diagram of a straight vertical wire carrying conventional current upwards, with circular magnetic field lines around it. Show four observation positions: directly above, below, left, and right of the wire in the plane of the page. Label the field at each position using standard symbols: cross for into the page and dot for out of the page. Include an upward current arrow and a clearly illustrated right-hand grip around the wire.]

### What do the dot and cross symbols mean?

Magnetic field diagrams often use two symbols to represent directions perpendicular to the page:

- **A cross (×)** means into the page, away from you.
- **A dot (•)** means out of the page, towards you.

Think of an arrow travelling through the page. If its point is heading towards you, you see its tip as a dot. If it is travelling away, you see its tail as a cross.

These symbols are particularly useful when a question asks for the magnetic field above or below a wire, because the field is pointing towards or away from you rather than left or right.

[IMAGE: Close-up visual comparison of a dot and a cross representing a vector perpendicular to a page. Show a small arrow pointing towards the viewer with a visible arrowhead and a second arrow pointing away with its tail visible. Label out of the page (•) and into the page (×).]

### Why does the direction reverse?

The magnetic field travels in circular paths around the wire.

With conventional current upwards, the field circles in one particular direction. At two positions on opposite sides of the wire, the circular field is pointing in opposite directions.

This is why the field above the wire is into the page, while the field below it is out of the page.

You can check the result without memorising the four entries in the table: return to the right-hand grip rule and examine where your fingers point at each position.

Now need research.### Important: get the wire orientation right

There is one important geometric correction to the opening setup. In the standard HSC diagram, the wire is drawn horizontally across the page, so that above and below mean opposite sides of the wire in the plane of the page. A vertical wire would make those positions lie along the wire, not on opposite sides.

Use this standard arrangement for the rest of the article:

Notice that reversing the current reverses both magnetic field directions. The field at each position doesn’t stay fixed when the current changes.

Also, be careful with the word above. In this article, it means above the wire as drawn on the page. In an actual laboratory, a compass can be physically positioned above or below a wire, which is a different three-dimensional arrangement.

A reliable three-step method

For almost any HSC question involving the magnetic field around a straight wire, follow this process.

Step 1: Identify conventional current.

Find the direction of conventional current, not necessarily the direction electrons move.

If a question gives electron flow, reverse its direction to obtain conventional current.

Step 2: Point your right thumb along the current.

Position your hand so your thumb follows the wire’s current direction.

Step 3: Read the direction of your curled fingers at the observation point.

Don’t just memorise that above means out of the page. That is only true for current flowing to the right.

If the current reverses, the answer reverses too.

02Why does a current-carrying wire produce a magnetic field?

This relationship was established experimentally, rather than simply assumed.

In 1820, Danish physicist Hans Christian Ørsted observed that an electric current could deflect a nearby compass needle. His observation provided evidence that electricity and magnetism were connected.

The interesting part was the arrangement of the apparatus.

What was the experiment testing?

The apparatus consisted of:

• A straight conducting wire positioned parallel to a compass needle.
• A battery connected to the wire through a switch.
• A compass positioned close to the wire.
• Connecting leads completing the circuit.

Before the switch was closed, the compass needle aligned approximately with Earth’s magnetic field.

The prediction was straightforward: if the current in the wire produced no magnetic field, closing the switch should not cause a systematic change in the compass direction.

But the needle deflected when current flowed.

When the current direction was reversed, the deflection also reversed. When the current stopped, the needle returned approximately to its original direction.

This showed that the current produced a magnetic field and that reversing the current reversed the field direction.

Why didn’t the compass point exactly along the wire’s magnetic field?

This is an important experimental detail.

A compass responds to the combined magnetic field acting on it. That includes Earth’s magnetic field as well as the field produced by the wire.

The needle aligns with the resultant magnetic field, not necessarily with the wire’s field alone.

Consider a wire running north-south, directly above a compass. The wire’s current flows northwards.

At the compass, which is physically below the wire, the wire’s magnetic field points west. Earth’s horizontal magnetic field points north.

The compass therefore points somewhere between north and west.

This also explains why you shouldn’t confuse the classic compass experiment with the earlier dot-and-cross diagram. They use different observation positions and different orientations.

What needed controlling in a repeat experiment?

A practical complication is the return wire.

Current must travel from the battery through the test wire and back to the battery. The return lead also produces a magnetic field. If it runs close to the compass, its field can affect the result.

A controlled repeat should therefore:

• Keep the return lead away from the compass, or route the outgoing and return leads together away from the test region.
• Keep the compass and test wire in fixed positions.
• Compare the compass direction with the current switched off and on.
• Reverse the current while keeping the apparatus unchanged.

Reversing the current is especially useful. Earth’s magnetic field stays approximately constant, while the wire’s field reverses. This helps distinguish the effect of the wire from the background field.

The historical observation established the connection between current and magnetism. The right-hand grip rule gives us a systematic way to predict the field direction at any position around an ideal straight wire.

For a broader explanation of the circular field pattern, see Magnetic Field Around a Current-Carrying Wire: HSC Physics.

03Worked examples

04Magnetic field direction is not magnetic force direction

This distinction catches students who remember a hand rule but apply the wrong one.

The right-hand grip rule tells you the direction of the magnetic field produced by a current.

Fleming’s left-hand rule tells you the direction of the force on a current-carrying conductor in an external magnetic field.

These are different questions.

A useful way to recognise the difference is to look at what information the question gives you.

If it gives a wire’s current and asks about the field around that wire, use the right-hand grip rule.

If it gives an external magnetic field and asks which way a wire or charged particle moves, you’re dealing with magnetic force.

Don’t use the direction of a force to decide the direction of the field unless the question gives enough additional information to work backwards.

For further practice with the distinction between electron flow and conventional current, see Electron Flow vs Conventional Current in HSC Magnetic Questions.

Common mistakes to avoid

04Questions and solutions

Question 1

A straight horizontal wire carries a conventional current towards the right.

Point P is directly above the wire, and point Q is directly below it.

Determine the magnetic field direction at both points.

Solution 1

The field at P points out of the page, while the field at Q points into the page.

Use the right-hand grip rule.

• Point your right thumb towards the right, following conventional current.
• Curl your fingers around the wire.
• At P, above the wire, your fingers indicate out of the page.
• At Q, below the wire, your fingers indicate into the page.

Therefore:

\[ P:\ \bullet \qquad Q:\ \times \]

The field directions are opposite because P and Q are on opposite sides of the circular magnetic field.

Question 2

A straight horizontal wire carries a steady conventional current. At point P, directly below the wire, the magnetic field is measured to be out of the page.

(a) Determine the direction of conventional current.

(b) State the magnetic field direction at point Q, directly above the wire.

(c) A student claims that the current must flow towards the right because the magnetic field points out of the page. Explain the error in this reasoning.

Solution 2

The conventional current flows to the left, and the magnetic field at Q points into the page.

Step 1: Work backwards from the known field direction.

We know the field at P, below the wire, points out of the page.

From the right-hand grip rule, this happens when conventional current flows to the left.

Step 2: Determine the field at Q.

Q is above the wire.

For a leftward current, the field above the wire points into the page.

Step 3: Identify the student’s mistake.

The student has memorised a result without considering the observation position.

A rightward current produces an out-of-page field above the wire, not below it.

The position of the observation point matters just as much as the direction of the current.

The correct answers are:

• (a) Conventional current flows left.
• (b) Magnetic field at Q points into the page.
• (c) The student has confused the field direction above the wire with the field direction below it.

Question 3

A straight horizontal wire carries conventional current towards the east (right).

A positively charged particle is located directly north (above) the wire. It moves northwards, parallel to the page.

(a) Determine the magnetic field direction at the particle.

(b) Determine the direction of the magnetic force on the positive particle.

(c) If the particle is replaced with an electron moving at the same velocity, what happens to the force direction? Does the magnetic field direction change?

Solution 3

The magnetic field points out of the page, the positive particle experiences a force towards the east, and the electron experiences a force towards the west. The magnetic field direction does not change.

Step 1: Determine the magnetic field.

The conventional current flows right.

The particle is above the wire.

Using the right-hand grip rule, the field points out of the page.

Step 2: Determine the force on the positive particle.

The particle moves northwards, while the magnetic field points out of the page.

These directions are perpendicular.

For a positive charge, the magnetic force follows the direction of the cross product:

\[ \vec F=q(\vec v\times\vec B) \]

Here:

• \(\vec F\) is magnetic force.
• \(q\) is the particle’s charge.
• \(\vec v\) is its velocity.
• \(\vec B\) is the magnetic field.

Using the right-hand cross-product rule, point your fingers north and curl them towards the field direction, out of the page.

Your thumb points east.

Therefore, the force on the positive particle is towards the east.

Step 3: Consider the electron.

An electron has negative charge.

Its magnetic force acts in the opposite direction to the force on a positive particle moving with the same velocity in the same field.

Therefore, the electron experiences a force towards the west.

The field itself remains unchanged because it is produced by the wire’s conventional current, not by the sign of the test particle’s charge.

This question tests two separate ideas: finding a magnetic field and finding the force exerted by that field.

Question 4

A straight wire is positioned directly above a compass on a horizontal table. The wire runs north-south and is parallel to the compass needle.

Earth’s horizontal magnetic field points north.

When the switch is closed, the north end of the compass needle deflects west of north.

(a) Determine the direction of conventional current in the wire.

(b) Predict the direction of compass deflection if the current is reversed.

(c) Explain why the compass needle does not point exactly west when the current is switched on.

Assume the wire’s magnetic field is strong enough to produce a measurable deflection but does not overwhelm Earth’s horizontal field.

Solution 4

The conventional current flows northwards. Reversing the current makes the compass deflect east of north. The needle does not point exactly west because it responds to the resultant of the wire’s field and Earth’s magnetic field.

Step 1: Identify the wire’s magnetic field direction.

The wire is north-south, and the compass is physically below it.

For a current flowing northwards, the right-hand grip rule gives a magnetic field towards the west at the compass.

Therefore, the observed westward deflection is consistent with northward conventional current.

Step 2: Reverse the current.

If the current flows south instead, the wire’s magnetic field at the compass reverses.

It now points east.

The compass needle therefore deflects east of north.

Step 3: Explain the compass direction.

Two magnetic fields act on the compass:

• Earth’s magnetic field points north.
• The wire’s magnetic field points west.

The compass aligns with their vector resultant, which points northwest.

This is a good example of why experimental observations and theoretical predictions are not always represented by a single direction arrow. The compass shows the combined effect of both fields.

Question 5

Two long, straight, parallel wires, A and B, lie horizontally in the plane of the page.

Wire A is positioned 4.0 cm directly above wire B.

Both wires carry conventional currents of equal magnitude, 6.0 A.

Initially:

• Wire A carries current towards the right.
• Wire B carries current towards the left.

Two observation points are defined:

• P is exactly halfway between the two wires.
• Q is 2.0 cm above wire A, meaning it is 2.0 cm from A and 6.0 cm from B.

Assume the wires are sufficiently long for the long-wire model to apply. For this model, magnetic field strength is proportional to \(I/r\), where \(I\) is current and \(r\) is perpendicular distance from the wire.

(a) Determine the direction of the resultant magnetic field at P.

(b) Determine the direction of the resultant magnetic field at Q.

(c) A switch now reverses the current in wire B only. Its current magnitude remains 6.0 A. Determine the new resultant field direction at both P and Q.

(d) Explain why the initial fields at P reinforce each other, even though the two wires carry currents in opposite directions. Your explanation should also account for why the fields at Q initially oppose each other.

Solution 5

Initially, the resultant field at P points into the page, while the resultant field at Q points out of the page. After reversing wire B’s current, the fields cancel at P and reinforce out of the page at Q.

This question requires you to consider the magnetic field produced by each wire separately before combining them.

Step 1: Determine the field from each wire at P.

P lies below wire A.

Wire A carries current to the right, so its field at P points into the page.

P also lies above wire B.

Wire B carries current to the left, so its field at P also points into the page.

Both fields point in the same direction.

Therefore, they reinforce each other, producing a resultant field into the page.

Step 2: Determine the field from each wire at Q.

Q lies above both wires.

For wire A, the current flows right, so its field at Q points out of the page.

For wire B, the current flows left, so its field at Q points into the page.

The two fields oppose each other.

However, they are not equally strong.

Step 3: Compare the field strengths at Q.

Both currents have the same magnitude.

However, Q is 2.0 cm from A and 6.0 cm from B.

Since the field strength is proportional to \(I/r\), the field from A is three times stronger than the field from B.

Let \(B_0\) represent the field strength produced by either wire at a distance of 2.0 cm.

The field contributions at Q are therefore:

\[ B_A=B_0 \]

\[ B_B=\frac{B_0}{3} \]

The fields oppose each other, so subtract their magnitudes:

\[ B_{\text{resultant}} =B_0-\frac{B_0}{3} \]

\[ B_{\text{resultant}}=\frac{2B_0}{3} \]

The stronger field from A determines the resultant direction.

Therefore, the field at Q points out of the page.

Step 4: Reverse the current in wire B.

Now both wires carry conventional current towards the right.

Consider P first.

• Wire A produces a field into the page at P.
• Wire B produces a field out of the page at P.

The distances from P to both wires are equal, and their current magnitudes are equal.

Their fields therefore have equal magnitudes and opposite directions.

They cancel completely:

\[ B_{\text{resultant at P}}=0 \]

Now consider Q.

Q is above both wires, and both currents flow to the right.

Both magnetic fields point out of the page.

They reinforce each other:

\[ B_{\text{resultant at Q}} =B_0+\frac{B_0}{3} \]

\[ B_{\text{resultant at Q}} =\frac{4B_0}{3} \]

The resultant field points out of the page.

Step 5: Explain the apparent contradiction.

The tempting assumption is that opposite currents always produce magnetic fields that cancel.

That isn’t correct.

The magnetic field direction depends on two things:

1. The direction of conventional current.
2. The observation point’s position relative to each individual wire.

At P, the two initially opposite currents produce fields in the same direction because P lies between the wires.

At Q, the fields oppose because Q lies outside both wires.

This is the key idea: you cannot determine the resultant magnetic field just by comparing the directions of the currents. You must find the field from each wire at the actual observation point, then combine the fields.

05The method to remember in an exam

When a question asks for the magnetic field direction above or below a straight wire, use this checklist:

1. Identify conventional current. Reverse electron flow if necessary.
2. Point your right thumb along the conventional current.
3. Curl your fingers around the wire.
4. Read the direction at the observation point.
5. Use a dot for out of the page and a cross for into the page.
6. If multiple wires are present, determine each field separately before combining them.

For a single horizontal wire, the essential results are:

Once you’re comfortable finding the field around one wire, the next useful skill is magnetic field superposition: combining fields from multiple wires, as in Question 5. From there, you can move on to determining the magnetic force on a current-carrying conductor in an external magnetic field.